Problem: $6ef - 2eg - 10e + 3 = 3f + 2$ Solve for $e$.
Answer: Combine constant terms on the right. $6ef - 2eg - 10e + {3} = 3f + {2}$ $6ef - 2eg - 10e = 3f - {1}$ Notice that all the terms on the left-hand side of the equation have $e$ in them. $6{e}f - 2{e}g - 10{e} = 3f - 1$ Factor out the $e$ ${e} \cdot \left( 6f - 2g - 10 \right) = 3f - 1$ Isolate the $e$ $e \cdot \left( {6f - 2g - 10} \right) = 3f - 1$ $e = \dfrac{ 3f - 1 }{ {6f - 2g - 10} }$ We can simplify this by multiplying the top and bottom by $-1$. $e= \dfrac{-3f + 1}{-6f + 2g + 10}$